Adaptive control system having hedge unit and related apparatus and methods

ABSTRACT

The invention includes an adaptive control system used to control a plant. The adaptive control system includes a hedge unit that receives at least one control signal and a plant state signal. The hedge unit generates a hedge signal based on the control signal, the plant state signal, and a hedge model including a first model having one or more characteristics to which the adaptive control system is not to adapt, and a second model not having the characteristic(s) to which the adaptive control system is not to adapt. The hedge signal is used in the adaptive control system to remove the effect of the characteristic from a signal supplied to an adaptation law unit of the adaptive control system so that the adaptive control system does not adapt to the characteristic in controlling the plant.

CROSS-REFERENCE TO RELATED APPLICATION

This application claims priority benefits of provisional application No.60/199,615 filed Apr. 25, 2000 naming Eric Norman Johnson and Anthony J.Calise as inventors.

STATEMENT OF U.S. GOVERNMENT RIGHTS IN THE INVENTION

This invention was made with U.S. Government funding under Contract No.NAG8-1638 awarded by the National Aeronautics and Space Administration(NASA)-Marshall Space Flight Center and Contract No. F49620-98-1-0437awarded by the Air Force Office of Scientific Research (AFOSR). The U.S.Government has certain rights in the invention.

FIELD OF THE INVENTION

The invention is directed to an adaptive control system and relatedmethod. More particularly, the invention is directed to an adaptivecontrol system with the capability to prevent or reduce undesiredadaptation of a control system due to selected characteristic(s) of theplant or control system.

BACKGROUND OF THE INVENTION

Adaptive control systems have the capability to adapt control responseto changing conditions within the plant being controlled or the plant'soperating environment. Adaptation to changing plant or environmentalconditions provides enhanced control response for many kinds of plants,and may be required for certain types of plants that cannot becontrolled with static control systems. However, conventional adaptivecontrol systems have a tendency to adapt to plant or control systemcharacteristics to which they should not. The control response ofadaptive control systems can be greatly diminished when subjected tocertain characteristic(s) of the plant or system, and can be renderedunstable in attempting to adapt to these characteristics. An example ofa characteristic that could adversely affect an adaptive control systemis a control or authority limit imposed on the control elements of anadaptive control system. If an operator generates a command signal thatexceeds the ability of the control system or plant to respond,adaptation of the control system can render the control system unstable.It is desirable to reduce or prevent the impact of suchcharacteristic(s) from adversely affecting the adaptive control system'sperformance.

SUMMARY OF THE INVENTION

The methods, apparatus, and system, of the invention overcome thedisadvantages noted above.

A first method of the invention comprises generating a hedge signal toavoid adaptation to a characteristic of at least one of an adaptivecontrol system and a plant controlled by such system. The first methodcan comprise modifying a commanded state signal with the hedge signal.The first method can also comprise generating a reference model statesignal using the commanded state signal modified by the hedge signal.The first method also can comprise generating a tracking error signalbased on the reference model state signal and a plant state signal, andgenerating an adaptive control signal to adapt control response of theadaptive control system. Through compensation for the characteristic inthe tracking error signal, the adaptive control signal can be generatedso as not to significantly adapt to the characteristic. Hence acharacteristic of the plant or control system that would impair or bedetrimental to control system's performance and/or stability can behedged out of the adaptive portion of the control system to preventadverse impact on control of the plant. The hedge signal can begenerated based on a difference between a first signal derived from aplant model not having the characteristic to be hedged, and a secondsignal derived from a plant model having the characteristic. The firstsignal can generated based on an input control signal and a plant statesignal in addition to the plant model not having the characteristic. Thesecond signal can be generated using a command control signal and aplant state signal, in addition to the plant models with thecharacteristic. The input control signal can be generated based on acommanded state signal, a plant state signal, and an adaptive controlsignal, and the command control signal can be generated using the inputcommand signal modified by a control allocation and a controlcharacteristic imposed by a controller. The input control signal andcommand control signal can be used to hedge a characteristic of thecontrol system to which adaptation is not to be performed. The methodcan also include generating a display based on the input control signal.An operator can use the display to generate a command control signal. Inthis aspect of the invention, the operator's control and response can behedged.

A second method of the invention is executed by an adaptive controlsystem. The second method comprises generating an input control signalbased on a commanded state signal, a plant state signal, and an adaptivecontrol signal. The second method also comprises generating a commandcontrol signal based on a commanded state signal, a plant state signal,an adaptive control signal, and further based on control allocation anda control characteristic of a controller used to generate the commandcontrol signal. The second method further comprises supplying thecommand control signal to an actuator, controlling a state of the plantbased on the command control signal, sensing a state of the plant, andgenerating a plant state signal based on the sensing of the plant. Thesecond method comprises generating a first signal based on the inputcontrol signal, the plant state signal, and a plant model without aplant characteristic to which the adaptive control system is not toadapt. The second method also comprises generating a second signal basedon the command control signal, the plant state signal, and a plant modelwith the plant characteristic to which the adaptive control system is toadapt. The second method further comprises generating a hedge signal bydifferencing the first and second signals, and generating a referencemodel state signal by modifying the commanded state signal with thehedge signal to include the effect of the control allocation and controlcharacteristic on plant state from the reference model state signal. Thesecond method further comprises comparing the plant state signal and thereference model state signal, generating a tracking error signal basedon the comparing step, and generating the adaptive control signal basedon the tracking error signal. The second method can comprise generatinga reference model signal based on the commanded state signal, the hedgesignal, and a reference model signal derived from a reference modelrepresenting the target response of the plant, the reference modelsignal to generate the input control signal. The second method can alsocomprise generating a reference model signal based on the commandedstate signal, the hedge signal and a reference model signal derived froma reference model representing the target response of the plant, thereference model signal, to generate the command control signal. Thesecond method can also comprise generating a linear control signal basedon the tracking error signal, generating a reference model signal basedon the commanded state signal, the hedge signal, and a reference model,and generating a pseudo- control signal based on the linear controlsignal, the reference model signal, and the adaptive control signal, andthe pseudo-control signal. The adaptive control signal can be generatedwith the plant state signal. The adaptive control signal can begenerated with a neural network having connection weights adjusted basedon the tracking error signal and the pseudo-control signal. The neuralnetwork maps the plant state signal to the adaptive control signal. Theplant state signal can also be used to generate the adaptive controlsignal. The second method can comprise generating the commanded statesignal based on a control action from an operator. The operator can behuman, and the method can comprise generating a display based on theplant state signal. The display can be used by the operator to generatethe commanded state signal. The second method can comprise generatingthe commanded state signal based on a signal generated by an operatorthat is a computer. The second method can also comprise generating adisplay for an operator based on the input control signal so that theoperator can generate the command control signal based on the display.

An apparatus of the invention can be used in an adaptive control systemfor controlling a plant. The apparatus is a hedge unit coupled toreceive at least one control signal and a plant state signal. The hedgeunit generates a hedge signal based on the control signal, the plantstate signal, and a hedge model including a first model having acharacteristic to which the adaptive control system is not to adapt, anda second model not having the characteristic to which the adaptivecontrol system is not to adapt. The hedge signal can be used in theadaptive control system to remove the characteristic from a signalsupplied to an adaptation law unit of the adaptive control system sothat the adaptive control system does not adapt to the characteristic incontrolling the plant. The characteristic to be hedged by the hedge unitcan be a time delay between generation of the commanded state signal bythe controller at a time, and receipt by the controller of the plantstate signal resulting from the commanded state signal generated at thetime. Also, the characteristic can be a time delay between generation ofa state by the plant and sensing of the state of the plant by the sensorto generate the plant state signal. Alternatively, the characteristiccan pertain to a control limit of the actuator used to control theplant. The control limit can be due to actuator end points, actuatordynamics, a rate limit of the actuator, or quantization effectsassociated with the actuator, for example.

An adaptive control system of the invention is coupled to receive acommand state signal indicative of a target state of a plant controlledby the adaptive control system. The adaptive control system comprises acontroller coupled to receive the commanded state signal, a plant statesignal, and an adaptive control signal. The controller generates aninput command signal based on the commanded state signal, the plantstate signal, the adaptive control signal, and a control model. Thecontroller generates a command control signal based on the commandedstate signal, the plant state signal, the adaptive control signal, thecontrol model, control allocation of the controller, and at least onecontrol characteristic of the controller. The controller is coupled tosupply the command control signal to the plant to control the plant'sstate. The actuator is coupled to receive the command control signal,and affects physical control of the plant's state using the commandcontrol signal. The adaptive control system can comprise a sensorcoupled to sense the plant state, that generates a plant state signalbased on the sensed plant state. The adaptive control system alsocomprises a hedge unit coupled to receive the input control signal, thecommand control signal, and the plant state signal. The hedge unitgenerates a hedge signal to modify the command state signal based on theinput control signal, the command control signal, the plant statesignal, and a hedge model indicative of a characteristic of at least oneof the plant and the adaptive control system, to remove the effect ofthe characteristic on a tracking error signal. The adaptive controlsystem also comprises a reference model unit coupled to receive thecommand state signal and the hedge signal. The reference model unitgenerates a reference model state signal based on the commanded statesignal and a hedge signal. The adaptive control unit also comprises acomparator unit coupled to receive the reference model state signal andthe plant state signal. The comparator unit generates a tracking errorsignal based on a difference between the plant state signal and thereference model state signal. The adaptive control system also includesan adaptation law unit coupled to receive the tracking error signal. Theadaptive control system generates the adaptive control signal based onthe tracking error signal. The adaptation law unit is coupled to supplythe adaptive control signal to the controller. The controller cangenerate the input control signal and the command control signal furtherbased on the reference model state signal. The characteristic to behedged by the adaptive control system can be time delay betweengeneration of the commanded state signal by the controller at aparticular time, and receipt by the controller of the plant state signalresulting from the commanded state signal generated at the particulartime. Alternatively, the characteristic can be a time delay betweengeneration of a state by the plant in response to the command controlsignal, and sensing of the state of the plant resulting from the commandcontrol signal. Further, the characteristic can be a control limit ofthe actuator used to control the plant. The control limit can be due toactuator end points, actuator dynamics, a rate limit of the actuator, orquantization effects of the actuator, for example. The commanded statesignal can be generated by an operator, and the adaptive control systemcan comprise an operator interface unit coupled to receive the plantstate signal. The operator interface unit relays the plant state to theoperator. The command unit can be used by the operator to generate thecommand state signal based on the operator's control action. Theoperator interface can be a display generated based on the plant statesignal. The operator can be a human being that generates the controlaction to the command unit to generate the commanded state signal. Thecommanded state signal is generated by a machine operator based on theplant state signal. The adaptation law unit can comprise a neuralnetwork having connection weights determined by the tracking errorsignal. The neural network can map the plant state signal to theadaptive control signal based on the connection weights to generate theadaptive control signal. The controller can generate a pseudo-controlsignal based on the commanded state signal and the plant state signal.The controller can be coupled to supply the pseudo-control signal to theneural network to adjust the connection weights of the neural network.The controller can comprise a dynamic inversion unit to generate thecommand control signal.

These together with other objects and advantages, which will becomesubsequently apparent, reside in the details of construction andoperation of the invented methods, apparatus, and article as more fullyhereinafter described and claimed, reference being made to theaccompanying drawings, forming a part hereof, wherein like numeralsrefer to like parts throughout the several views.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a general block diagram of the adaptive control system of theinvention that uses a hedge signal to hedge against a characteristic towhich the adaptive control system is not to adapt;

FIG. 2 is a block diagram of a controller of the adaptive control systemthat generates a command control signal to control an actuator affectinga state of a plant;

FIG. 3 is a block diagram of a hedge unit of the adaptive controlsystem;

FIG. 4 is a block diagram of a reference model unit of the adaptivecontrol system;

FIG. 5 is a view of a processor-based system for implementing theadaptive control system of FIGS. 1-4;

FIG. 6 is a flowchart of a method of the invention used to generate ahedge signal to prevent or reduce adaptation of the adaptive controlsystem of FIGS. 1-4 to the characteristic that is to be hedged;

FIG. 7 is a block diagram of an adaptive control system that includes aneural network for generating an adaptive control signal based on atracking error signal and a pseudo-control signal;

FIG. 8 is a relatively detailed block diagram of a hedge unit used withthe adaptive control system of FIG. 7;

FIG. 9 is a relatively detailed block diagram of a reference model unitused to implement a second-order reference model to generate a targetreference model state response to a commanded state signal;

FIG. 10 is a relatively detailed view of a neural network that can beused to map a tracking error signal and a plant state signal to anadaptive control signal using connection weights set adaptively based ona tracking error signal, a pseudo-control signal, and the plant statesignal; and

FIG. 11 is a block diagram of a control and allocation andcharacteristic unit in a special case in which an operator is includedin the unit.

DETAILED DESCRIPTION OF THE INVENTION

As used herein, the following terms have the following definitions:

“Actuator” can be virtually any device capable of affecting the state ofa plant to control a degree of freedom thereof. Such actuator can be amotor, motor-driven screw, a hydraulic cylinder, a pump or valvecontrolling a stream of air, a thermal heater, a compressor or suctiongenerator, or other device.

“Adaptive control system” means a control system having the capabilityto adapt to changes in a controlled plant or its environment over time.

“Characteristic” is a property of a plant or control system that has aneffect for which adaptation of the control system is not to beperformed. The characteristic can be a time delay between generation ofa command signal and sensing and report of the plant state resultingfrom the command signal to the control system. The characteristic canalso be a control limit such as actuator end points, e.g., extremepositions, temperatures, pressures, etc. obtainable by the actuator,actuator dynamics, rate limits, quantization effects, and possiblyothers. The characteristic can also be a feature of a sensor, forexample, the time delay from change of a plant state to sensing of thatchanged plant state by the sensor. The characteristic can also be anoperator's control or response.

“Control limit” is a limit on the capability of a control system tocontrol a plant. A control limit can also be imposed by limitations inthe actuators used to control the plant. These limitations can includeactuator end points, e.g., extreme positions, temperatures, pressures,etc. obtainable by the actuator, actuator dynamics, rate limits,quantization effects, and possibly others. Control limits could also beimposed intentionally for a variety of reasons. Adaptive control systemsare sensitive to control limits that can cause the adaptive controlsystems to lose stability. The invention provides the capability tocompensate for control limits to permit stable control of the plant withthe adaptive control system.

“Hedge” means to reduce or prevent adaptation of an adaptive controlsystem to a characteristic.

“Hedge model” is a model of one or more elements of the system or plantwith and without a characteristic that is to be hedged. A hedge modelmay be a model of a plant, a control system, e.g., an actuator orsensor, an operator, or any other feature of the control system or plantto which the control system is not to adapt.

“Operator” can be a human or computer, for example, that senses a plantstate using a plant state signal, and generates a commanded state signalto control the plant.

“Plant” refers to a system controlled by a control system. For example,the plant can be an aircraft, spacecraft, space-launch vehicle,satellite, missile, guided munition, automobile, or other vehicle. Theplant can also be a robot, or a pointing or orientation system such as asatellite orientation system to orient power-generation panels, atransceiver, or a docking mechanism. Such plant can also be a brakingsystem, an engine, a transmission, or an active suspension, or othervehicle subsystem. The plant could be a manufacturing facility or apower generation facility. The plant could also be virtually anycontrollable system.

“Sensor” can be virtually any device(s) for sensing a degree of freedomof a plant's state, whether alone or in combination with one or moreother sensors, to generate a measurement or estimate of plant state. Thesensor can be virtually any device suitable for sensing informationregarding a plant's state. For example, the sensor could be a gyroscopefor detecting orientation of a vehicle such as an aircraft, i.e., pitchor roll attitudes or side slip. The sensor can also be a temperature orpressure sensor, a position, velocity, or inertial sensor.

“(s)” means one or more of the thing meant by the word preceding “(s)”.Thus, characteristic(s) means one or more characteristics.

The adaptive control system 10 of FIG. 1 operates in a control cyclethat is repeatedly executed to control the plant 12 on an ongoing basis,at least until control is terminated. The basic function of the system10 is to generate a commanded control signal d_(cmd) using a commandedstate signal x_(r), a plant state signal x_(p) an adaptive controlsignal v_(ad), and optionally a reference model state signal x_(rm). Inthe case of the first execution of the control cycle, when previousvalues of the plant state signal x_(p) and the adaptive control signalv_(ad) are employed, they are assigned predetermined values,respectively. The commanded state signal x_(r) is used by the controller14 along with the plant state signal x_(p) and an adaptive controlsignal v_(ad) to generate at least one control signal d. If adaptationto one or more characteristics of the controller 14 is to be avoided,the controller 14 is implemented to generate an input control signald_(in) that is the control signal d generated by the controller 14before imposition of the characteristic(s) on such control signal, and acommand control signal d_(cmd) that is the input control signal d_(in),modified by the controller's characteristic. The controller 14 iscoupled to supply the command control signal d_(cmd) to the actuator 16that controls the state of the plant 12. The plant state is sensed bythe sensor(s) 18 to generate a plant state signal x_(p). The hedge unit20 is coupled to receive the input control signal d_(in) and the commandcontrol signal d_(cmd) for the control cycle under execution from thecontroller 14. In addition, the hedge unit 20 is coupled to receive theplant state signal x_(p), and optionally the actuator state signal x.The hedge unit 20 uses a plant model to predict the plant statesresulting from the input command signal d_(in) and the command controlsignal d_(cmd), and generates a hedge signal v_(h) based on a differencebetween these two predicted plant states. Therefore, the hedge unit 20generates the hedge signal v_(h) to isolate the contribution to plantstate that results from the presence of the control characteristic(s) inthe command control signal d_(cmd). In addition, the hedge unit 20 canimpose a plant model without one or more plant characteristic(s) forwhich adaptation is not to be performed by the system 10, and a plantmodel that includes the plant characteristic(s). By using the plantmodel without the plant characteristic to modify the input controlsignal d_(in) to generate a first signal and by using the plant modelwith the characteristic(s) to modify the command control signal d_(cmd)to generate a second signal, the hedge unit 20 can generate the hedgesignal v_(h) to isolate the contribution to plant state that resultsfrom the presence of the plant characteristic. The hedge unit 20 iscoupled to supply the hedge signal v_(h) to the reference model unit 22.The reference model unit 22 is also coupled to receive the commandedstate signal x_(r). The reference model unit 22 uses the hedge signalv_(h) and a reference model indicating the target state of the plantbased on the commanded state, to modify the commanded state signal x_(r)to include the contribution to plant state caused by thecharacteristic(s) to be hedged. The comparator 24 is coupled to receivethe reference model state signal x_(rm) and the plant state signalx_(p), and generates a tracking error signal e. The comparator 24 cangenerate the tracking error signal e by differencing the plant statesignal x_(p) and the reference model state signal x_(rm) to generate thetracking error signal e. The comparator 24 is coupled to supply thetracking error signal e to the adaptation law unit 26. Because thecharacteristic(s) for which no adaptation of control response is to bemade has been removed, at least partially, from the tracking errorsignal e, the adaptation law unit 26 will necessarily not adapt to suchcharacteristic(s). Accordingly, the presence of the characteristic(s)has no impact on performance of the adaptation law unit 26. Theadaptation law unit 26 generates an adaptive control signal v_(ad) basedon the tracking error signal e. The adaptation law unit 26 canoptionally be coupled to receive the plant state signal x_(p) asindicated by the broken line in FIG. 1, for use in generating theadaptive control signal v_(ad). In addition, the adaptation law unit 14can be coupled to receive a pseudo-control signal v_(pc) generated bythe controller 14 for use by the adaptation law unit 26 in generatingthe adaptive control signal V_(ad).

In FIG. 2, the controller 14 includes a control model 140 and a controlallocation and characteristic unit 142. The control model 140 and thecontrol allocation and characteristic unit 142 can be implemented assoftware modules within the hedge unit 14. The control model 140 isbasically a software implementation of the control law to be implementedby the adaptive control system 10 to control the plant 12. The controlmodel 140 is coupled to receive either the commanded state signal x_(r),or the reference model state signal x_(rm), and is also coupled receivethe plant state signal x_(p), and the adaptive control signal v_(ad).The control model 140 maps these signals to the input control signald_(in). Those of ordinary skill in the art will understand how togenerate a control law appropriate for a plant controlled by theadaptive control system 12. For example, the control model 140 can be alinear proportional plus derivative, or proportional plus integralcontrol law implemented in a software module or function. The controlmodel 140 is coupled to supply the input control signal d_(in) to thecontrol allocation and characteristic unit 142. The unit 142 maps theinput control signal d_(in) to the control signal d_(cmd). The unit 142can map the input control signal d_(in), to the control signal d_(cmd)so as to allocate control responsibility for the plant's controlleddegree of freedom based on a predetermined scheme. For example, theplant 12 could be an aircraft configured so the ailerons on both wingscan be controlled to achieve a commanded roll attitude. The unit 142 canserve to allocate the amount of aileron deflection to the two actuatorsthat control the wing ailerons so as to influence the roll attitudecommanded by the input control signal d_(in), The unit 142 can includethe on-line identification of a model of the plant and the optimal ornear-optimal allocation of multiply-redundant control effectors based onthe solution of an optimization scheme that employs either theidentified plant model or a stored model of the plant. The unit 142 canalso impart control characteristic(s) to the input control signal d_(in)to generate the control signal d_(cmd). Such control characteristic(s)could be control limits such as actuator end points that cannot beexceeded due to limitations of the actuator or associated controllinkages. Alternatively, the control characteristic(s) could beconservative authority limits placed on the control signal d_(in), toinsure the actuator end points are never encountered. For example, theactuator may be capable of moving a control surface by ±21 degrees ofangle. If the input control signal d_(in), designates 25 degrees ofangle, the unit 142 will clip the input control limit d_(in), to producea command control signal of 20 degrees of angle. Another control limitmay pertain to an actuator's rate limit. It is possible that the inputcommand signal d_(in), may command the actuator 16 to respond morerapidly than it is able. Accordingly, the unit 142 can be programmed togenerate the command control signal d_(cmd) to move the actuator 16 moregradually as compared to the input control signal d_(in). As anotherexample, the actuator 16 may be able to move only in quantized steps.The unit 142 can be used to map the control signal d_(in), to thecommand control signal d_(cmd) so that the command control signal isquantized. In addition, the unit 142 can be used to impose authoritylimits on the actuator 16. Thus, although an actuator 16 can be capableof actuation to the point of endangering the plant, the unit 142 can beused to impose a control limit on the actuator 16. Therefore, forexample, if the operator 30 is an auto-pilot monitored by a human pilotto take control in emergency situations, the auto-pilot can be limitedto control the aircraft plant 12 to limits set by the unit 142. Controllimits set by the unit 142 can also be imposed by the sensor 18. Forexample, if the actuator 16 can change the state of the plant 12 fasterthan the sensor 18 can sense the resulting changes, the unit 142 canlimit the input control signal d_(in) to generate the command controlsignal d_(cmd) to change the plant's state in a manner the sensor 18 canaccurately sense. Yet another example of a control limit is the finitetime required of a processor to process the various input signals to thecontroller and to generate the controller's output signals.

Turning now to FIG. 3, the hedge unit 20 includes a hedge model 200having a plant model 201 without the plant characteristic that is to behedged and a plant model 202 with the plant characteristic(s) thatis/are to be hedged, and a comparator 204. These elements of the hedgeunit 20 can be implemented as one or more software modules or functionswithin the hedge unit 20. The plant model 201 without thecharacteristic(s) is coupled to receive the input control signal d_(in),and the plant state signal x_(p). The plant model 202 with thecharacteristic(s) generates a first signal that indicates the predictedplant response to the input control signal d_(in) given the plant statesignal x_(p). The plant model 202 with the plant characteristic(s) thatis to be hedged is coupled to receive the command control signal d_(cmd)and the plant state signal x_(p). Based on these signals, the plantmodel 202 with the characteristic(s) to be hedged is used to generate asecond signal. The comparator 204 is coupled to receive the first signalfrom the plant model 201 not having the plant characteristic to behedged, and the plant model 202 having the characteristic(s) to behedged. The comparator 204 differences the first and second signals togenerate the hedge signal v_(h). The hedge signal v_(h) in effectisolates the plant and/or system characteristic(s) that are to behedged.

In FIG. 4, details of a possible implementation of the reference modelunit 22 are shown. The reference model unit 22 includes a referencemodel 220, a comparator 222, and a state computation unit 224. Thereference model 220 receives the commanded state signal x_(p), and thereference model state signal x_(rm) from the state computation unit 224.The reference model 220 generates a signal x_(r)′ based on the commandedstate signal x_(r) and the reference model state signal x_(rm). Thereference model 220 is a software module or function that maps thecommanded state signal x_(r), to the reference model state signalx_(rm). The reference model state signal x_(rm) represents the targetplant state corresponding to the commanded state signal x_(r). Thesignal x_(r)′ from the reference model 220 is supplied to the comparator222. The comparator 222 also receives the hedge signal v_(h) from thehedge unit 20. The comparator 222 subtracts the hedge signal v_(h) fromthe signal x_(r)′ to generate the signal x_(r)″. The signal x_(r)″ issupplied to the state computation unit 224. The state computation unit224 computes the reference model state signal x_(rm) from the signalx_(r)″. More specifically, the state computation unit 224 computesscalar, derivative and/or integral values of the signal x_(r)″ accordingto the form or order of the reference model. Accordingly, the statecomputation unit 224 generates the reference model state signal x_(rm)as a vector with scalar, integral and/or derivative terms using thecommanded state signal x_(r) as modified in the unit 22 by the hedgesignal v_(h), and the reference model 222. The state computation unit224 supplies the resulting reference model state signal x_(rm) orpredetermined terms thereof as a feedback signal to the reference model220. The state computation unit 224 also supplies the reference modelstate signal x_(rm) to the comparator 24. The reference model statesignal x_(rm) includes the reference model response to thecharacteristic to be hedged so that it can be used in the comparator 24to extract from the plant state signal x_(p) the contribution to plantstate resulting from the presence of the characteristic(s). Accordingly,the effect of the characteristic is eliminated or at least reduced fromthe tracking error signal e so that the adaptation law unit 26 will notadapt to the characteristic's impact on the system 10 or the plant 12.Of course, it may not be possible to remove all impact of thecharacteristic from the tracking error signal e. However, enough of theimpact of the characteristic should be removed from the tracking errorsignal e so that system control of the plant will not be compromised.Satisfaction of this objective depends upon pre-specifications for thesystem based on control performance objectives, control stability, andthe nature of the control system 10 and plant 12.

FIG. 5 is a possible implementation of the system 10. The actuator 16,the sensor 18, the operator interface unit 28, the command unit 32, aprocessor 34, and a memory 36 are coupled to a bus 38. The processor 34can be a microprocessor or a microcontroller, for example. For example,the processor 34 could be a microprocessor with 64-bit word sizeoperating at a 1.0 GHz instruction execution cycle. The processor 34 canbe a Pentium® III microprocessor commercially-available from IntelCorporation, Santa Clara, Calif., or an Athlon® microprocessor fromAdvanced Micro Devices®, Inc., Sunnyvale, Calif. The memory 36 stores acontrol program 360 and data 362. The control program 360 is executed bythe processor 34 in the performance of a control cycle of the adaptivecontrol system 10. The control program 360 includes the software modulesused to implement the controller 14, the hedge unit 20, the referencemodel unit 22, the comparator 24, and the adaptation law unit 26. Thedata 362 includes data used by the processor 34 in executing thesoftware modules of the control program 360 or temporary data generatedby the processor 34 as it executes the control program 360. In theoperation of the system 10 of FIG. 5, the sensor 18 has sensed the stateof plant 12 to generate the plant state signal x_(p). The plant statesignal x_(p) has been stored as data 362 stored in the memory 36 via thebus 38. Also, signals required for use in the next control cycle whichcould include the adaptive control signal v_(ad) and the plant statesignal x_(p) and possibly other signals as well, are stored as data 362in the memory 36. Alternatively, the adaptive control signal v_(ad) canbe generated in the control cycle under execution using a fixed-pointsolution. The command unit 32 writes the commanded state signal x_(r)for the current control cycle as data 362 stored in the memory 36. Inexecuting its control program 360 over the control cycle underexecution, the processor 34 reads the commanded state signal x_(r) fromthe memory 36. The processor 34 also reads the plant state signal x_(p)and the adaptive control signal v_(ad) and generates the input controlsignal d_(in) and the command control signal d_(cmd). Alternatively, theplant state signal x_(p) or a construction thereof from the sensorsignal derived from a time after execution of the previous control cyclecan be stored in memory for use in the next control cycle. The processor34 supplies the command control signal d_(cmd) to the actuator 16 thatcontrols the state of the plant 12 based thereon. The processor 34 alsoexecutes the control program 360 to generate the hedge signal v_(h)based on the input control signal d_(in) the command control signald_(cmd), the plant state signal x_(p), and optionally also on theactuator state signal x_(a). Processor 34 further executes the controlprogram 360 to generate the reference model state signal x_(rm),. Theprocessor 34 subtracts the reference model state signal x_(rm), from theplant state signal x_(p) to generate the tracking error signal e. Theprocessor 34 uses the tracking error signal e and optionally also theplant state signal x_(p) and a pseudo-command signal v_(pc), to generatethe adaptive control signal v_(ad). The processor 34 can store anysignals needed for the next control cycle in the memory 36.

The method of FIG. 6 follows operation of the adaptive control system 10of FIGS. 1-5 over a control cycle. In step S1 of FIG. 6, the methodbegins. In step S2 of FIG. 6, the command unit 32 generates thecommanded state signal xr based on the operator's action and/oroperator-generated signal. In step S3 the controller generates the inputcontrol signal d_(in) based on the commanded state signal x_(r), theplant state signal x_(p) from sensor 18 and the adaptive control signalv_(ad) generated by the adaptation law unit 26. Alternatively, thecommanded state signal x_(r) is first used by the reference model unit22 to generate the reference model state signal x_(rm). The controller14 generates the input control signal d_(in) based on the referencemodel state signal x_(rm), and the plant state signal x_(p) from thesensor 18, and the adaptive control signal v_(ad) generated by theadaptation law unit 26. In step S4 the controller 14 generates thecontrol signal d_(cmd) based on the commanded state signal x_(r), andthe plant state signal x_(p) and adaptive control signal v_(ad) usingthe control allocation and characteristic unit 142 of the controller 14.In optional step S5 the controller 14 generates a pseudo-control signalv_(pc) based on the commanded state signal x_(r), and the plant statesignal x_(p) and the reference model state signal x_(rm). In step S6,the controller 14 supplies the control signal d_(cmd) the actuator 16 tocontrol the plant 12. In step S7 the sensor 18 senses the plant state.In step S9 the controller 14 generates the plant state signal x_(p)based on the sensed plant state. In step S10 the processor 34 receivesthe plant state signal x_(p). In step S11 the hedge unit 20 generatesthe hedge signal v_(h) based on the input control signal d_(in), thecommand control signal d_(cmd), optionally on the actuator state signalx_(a), the plant model with the characteristic whose effect is to beremoved from the tracking error signal e supplied to the adaptation lawunit 26, and the plant model without the characteristic whose effect isto be removed from the tracking error signal. In step S12 the referencemodel unit 22 generates the reference model state signal x_(rm), basedon the commanded state signal x_(r), the hedge signal v_(h), and thereference model. In step S13 the comparator 24 generates the trackingerror signal e based on the plant state signal x_(p) and the referencemodel state signal x_(rm). In step S14 the adaptive law unit generatesthe adaptive control signal v_(ad) based on the tracking error signal eand/or the pseudo-control signal v_(pc) generated by the controller 14.In step S15, the processor 34 stores any signals required for the nextcontrol cycle in the memory 36. Such signals might include the plantstate signal x_(p) and the adaptive control signal v_(ad). In step S16the method of FIG. 6 ends.

FIGS. 7-13 are views of an exemplary embodiment of the adaptive controlsystem 10. In FIG. 7 the controller 14 comprises the control model 140and the control allocation and characteristic unit 142. The controlmodel 140 includes a linear control module 144, a summing unit 146, andan approximate dynamic inversion module 148. The linear control module144 generates a linear control signal v_(lc), based on the trackingerror signal e. More specifically, the linear control module 144 appliesa linear control law to map the tracking error signal e to the linearcontrol signal v_(lc). The reference model unit 22 generates thereference model signal v_(rm) that is a subset of the vector of thereference model state signal x_(rm). The linear control module 144 andthe reference model unit 22 are designed to control the plant 12 fortarget system response and stability using design techniques well-knownto those of ordinary skill in the art. In the exemplary embodiment ofFIG. 7, the adaptation control unit 26 includes a neural network 260.The neural network 260 receives as inputs the plant state signal x_(p)and a pseudo-control signal v_(pc), and the tracking error signal e. Theneural network 260 maps the plant state signal x_(p) to the adaptivecontrol signal v_(ad) using connection weights adaptively set eachcontrol cycle by the tracking error signal e and the pseudo controlsignal v_(c). By updating the connection weights of the neural network260 with successive control cycles, the system 10 is adaptive to changesover time in the plant 12 as well as the system 10. The pseudo-controlsignal v_(pc) is used in part to adapt the connection weights of theneural network 260 generated in the control model 140. In the controlmodel 140, the adaptive control signal v_(ad) is subtracted from the sumof the reference model signal v_(rm) and the linear control signalv_(ad) in the summing unit 146 to generate pseudo-control signal v_(pc). The pseudo-control signal v_(pc) is supplied to the hedge unit 20 foroptional use in generating the hedge signal v_(h). The pseudo-controlsignal v_(pc) is also supplied to a dynamic inversion unit 148 of thecontrol model 140. The dynamic inversion unit 148 inverts thepseudocontrol signal v_(pc) based on an inversion function representingthe plant control response. The inversion function is a function of theplant state signal x_(p) and the pseudo-control signal v_(pc). Theinversion function maps these signals to the input command signald_(in). The remainder of the adaptive control system 10 is similar infunction and configuration to previously described embodiments.

FIG. 8 is an exemplary embodiment of the hedge unit 20 of FIG. 7. Inthis embodiment, the first signal d₁ supplied to the comparator 204 canbe generated in one of two ways. More specifically, the plant statesignal x_(p) and the input command signal d_(in) can be supplied to theplant model 210 that includes an inversion function to generate thefirst signal d₁ based on these signals. Alternatively, thepseudo-control signal v_(pc) can be supplied as the first signal d₁directly to the comparator 204. The command control signal d_(cmd) issupplied to the plant model 202 that includes an actuator model 206 forone or more characteristics of the actuator 16 to be hedged, and a plantmodel 208 with one or more characteristics of the plant 12 to be hedged.The command control signal d_(cmd) is fed to the actuator model 206 togenerate command signal δ. The command signal δ is supplied to the plantmodel 208 along with the plant state signal x_(p) for use in generatingthe second signal d₂ supplied to the comparator 204. The comparator 204generates the hedge signal v_(h) by subtracting the first and secondsignals d₁, d₂ to isolate the effect of the characteristics to behedged.

In FIG. 9 a relatively detailed example of the reference model unit 22is shown. The reference model unit 22 in this case is second-order, andhas constant, derivative, and double derivative terms. The referencemodel unit 22 includes a comparator 222, a multiplier 226, a summingunit 228, integrators 230, 232, and multipliers 234, 236. The multiplier226 multiplies the commanded state signal x_(r) by a predeterminedconstant ω_(n) ² to generate a modified signal supplied to the summingunit 228. The summing unit 228 subtracts signals from the multipliers234, 236 from the modified signal from the multiplier 228 to generatethe reference model signal v_(rm). The summing unit 228 supplies thereference model signal v_(rm) to the controller 14. The summing unit 228also supplies the reference model signal v_(rm) to the comparator 222.The comparator 222 subtracts the hedge signal v_(h) from the referencemodel signal v_(rm) to generate a signal supplied to the integrator 230.The integrator 230 integrates the signal from comparator 222 to generateintegrated signal {dot over (x)}_(rm). The integrated signal {dot over(x)}_(rm) is supplied to the integrator 232 to generate the referencemodel state signal x_(rm) that in this case has a “constant” term, aderivative term, and a second-derivative term. The reference model statesignal x_(rm) is supplied to the comparator 24. The integrated signal{dot over (x)}_(rm) from the unit 230 is also supplied to the multiplier234 that multiplies this integrated signal by the constant 2ζω_(n) inwhich ζ and ω_(n) are constants, and supplies the resulting signal tothe summing unit 228. The “constant” term from the reference model statesignal x_(rm) is also supplied to the multiplier 236 that multipliesthis signal by the constant ω_(n) ² to generate a signal supplied to thesumming unit 228. The signals from multipliers 234, 236 are subtractedfrom the signal from multiplier 226 to generate the reference modelsignal v_(rm).

FIG. 10 is a diagram of a neural network 260. The neural network 260includes an input layer 262, a hidden layer 264, and an output layer266. The input layer 262 has N₁ nodes receiving elements of the plantstate signal {overscore (x)} and the pseudo-control signal v_(pc), N₁being a positive integer. The N₁th nodes of the input layer 262 aremultiplied by respective connection weights V to generate the inputsignals to the N₂ nodes of the hidden layer 264, N₂ being a positiveinteger. The weighted input signals to the hidden layer 264 are suppliedas input signals to the sigmoidal activation function σ(z) of the form:$\begin{matrix}{{\sigma (z)} = \frac{1}{1 + ^{- {az}}}} & (1)\end{matrix}$

in which a is a predetermined constant and z represents the V-weightedinput signals from the input layer 262. The outputs from the hiddenlayer 264 are weighted by the connection weights W, and are supplied asinput signals to respective nodes 1-N₃ of the output layer 266. Thesenodes add respective input signals to generate the adaptive controlsignal −v_(ad). The mapping of the plant state signal x_(p) to theadaptive control signal v_(ad) performed by the neural network 260 canbe expressed as: $\begin{matrix}{{v_{ad} = {y_{i} = {{\sum\limits_{j = 1}^{N_{2}}\quad {\left\lbrack {{w_{ij}{\sigma \left( {{\sum\limits_{k = 1}^{N_{1}}\quad {v_{jk}{\overset{\_}{x}}_{k}}} + b_{v_{j}}} \right)}} + b_{w_{i}}} \right\rbrack i}} = 1}}},2,\ldots \quad,N_{3}} & (2)\end{matrix}$

where N₁, N₂, N₃ are the number of nodes in the input, hidden, andoutput layers 262, 264, 266, respectively, referenced by correspondingindexes k, j, i. The connection weights v_(jk) and w_(ij) are setadaptively by the states of the tracking error signal e and the N₁inputs to the neural network input layer 262. The constants b_(vj) andb_(wi) are predetermined. In matrix form equation (2) can be expressedas:

v_(ad)=y=W^(T)σ(V^(T){overscore (x)})  (3)

in which {overscore (x)} is the neural network input signal, V^(T) isthe transpose of the connection weight vector V, σ is the sigmoidalactivation function, W^(T) is the transpose of the connection weightvector W, and y=v_(ad) is the adaptive control signal. The signal v_(ad)can either be multiplied by “−1” or mapped by the neural network 260 togenerate the signal −v_(ad) for supply to the controller 14.

The manner in which the tracking error signal e and the input layersignal are used to adapt the connection weights V and W is nowdescribed. The pseudo-control signal v_(pc) is generated using thereference model signal v_(rm), the linear control signal v_(lc), and theadaptive control signal v_(ad), as follows:

v_(pc)=v_(rm)+v_(lc)−v_(ad)  (4)

The pseudo-control signal v_(pc) is related to the acceleration term ofthe reference model state. The pseudo-control signal can be furtheraugmented by terms as may be required to support proof of boundedness.An example of a term is commonly referred to as the robustifying termand is well know to those of ordinary skill in the art. Dynamicinversion is used to reduce the control design problem to that of acontrol design for a linear, time-invariant plant. However, as iswell-known to those of ordinary skill in this technology, use of animperfect model in the dynamic inversion process can corrupt the desiredrelationship between acceleration of the plant state vector and thepseudo-control by an amount A often referred to as an inversion error.This relationship between acceleration of the plant state,pseudo-control, and the inversion error is defined in Equation (5).

{umlaut over (x)}_(p)=v_(pc)+Δ  (5)

The derivative of the tracking error signal e can be expressed as:

{dot over (e)}=Ae+b(Δ+v_(ad))  (6)

in which A is Hurwitz. The output of the neural network v_(ad) is usedto approximate the inversion error, Δ so that the error dynamics ofEquation (6) will remain bounded, and tracking error is minimized. Theconstant ζ is defined by the equation:

ζ=e^(T)Pb  (7)

in which e^(T) is the transpose of the tracking error signal e, b is apredetermined matrix constant from Equation (6), and P is the solutionof a Lyapunov equation (8).

A^(T)P+PA=−Q  (8)

in which Q is a positive definite matrix. The adaptation law forupdating the neural network weights and implemented by the adaptationlaw unit 26 can be expressed as:

{dot over (V)}=−└{overscore (x)}ζW^(T) σ′+λ_(v)|ζ|V┘Γ_(v)  (9)

{dot over (W)}=−Γ_(W[(σ−σ′V) ^(T){overscore (x)})ζ+λ_(W)|ζ|W]  (10)

in which {dot over (V)} is the derivative of the connection weightvector V of the neural network 260, {dot over (W)} is the derivative ofthe W weight vector of the neural network 260, σ′(z) is the partialderivative of sigmoidal function σ(z) with respect to z, λ_(V), λ_(W),ζ, Γ_(V), Γ_(W) are predetermined vectors, and x is the plant statesignal.

For the case of a second-order reference model (FIGS. 7-10 ) theremaining characteristics are:

{umlaut over (x)}_(p)=ƒ(x_(p), {dot over (x)}_(p),d_(cmd)(d_(in)))  (11)

{umlaut over (x)}_(rm)=v_(rm)−v_(h)=ƒ_(rm)(x_(rm), {dot over (x)}_(rm),x_(r))−v_(h)  (12)

v_(lc)=K_(p)(x_(rm)−x_(p))+K_(D)({dot over (x)}_(rm)−{dot over(x)}_(p))  (13)

v_(pc)=v_(rm)+v_(lc)−v_(ad)  (14)

v_(h)=v_(pc)−(x_(p), {dot over (x)}_(p), d_(cmd)(d_(in)))  (15)

d_(in)=⁻¹(x_(p), {dot over (x)}_(p), v_(pc))  (16)

in which K_(p) and K_(d) are predetermined constants. Equation (16)corresponds to the dynamic inversion unit 148 of FIG. 7. The trackingerror signal e can be expressed as the vector of differences:$\begin{matrix}{e = \begin{bmatrix}{{\overset{.}{x}}_{rm} - {\overset{.}{x}}_{p}} \\{x_{rm} - x_{p}}\end{bmatrix}} & (17)\end{matrix}$

It can be shown that whether δ=d_(in)=d_(cmd) or δ=d_(in), ≠d_(cmd), thefollowing equation holds:

{dot over (e)}=Ae+b└Δ(x_(p), {dot over (x)}_(p), d_(cmd))+v_(ad)┘  (18)

Hence, due to the hedge signal vh generated by the hedge unit 20, theadaptive control system 10 is bounded with respect to tracking error andneural network weights. The plant will track the desired response asclose as is possible within the limits of d_(cmd). Without the hedgeunit 20, it can be shown that the system 10 would not be stable forcases in which d_(in)≠d_(cmd).

In FIG. 11 a special case of the control allocation and characteristicunit 142 is shown. More specifically, the unit 142 includes an operatorinterface unit 144, and operator 146, and a command unit 148. Theoperator interface unit 144 receives the input command signal d_(in) andthe plant state signal x_(p) and generates a signal or display based onthese signals. The operator 146 can be a human operator, a computer, orother machine, for example. In the case of a human operator, theoperator interface unit generates a display based on the input commandsignal d_(in) and the plant state signal x_(p). The operator 146 usesthe display from the operator interface unit 144 to control the commandunit 148 to generate the command control signal d_(cmd). The commandcontrol signal d_(cmd) is supplied to the actuator 16 to control thestate of the plant. The configuration of the unit 142 in FIG. 11 isuseful in numerous contexts. For example, in an aircraft, it may bedesirable to have an auto-pilot whose control of the aircraft islimited. In situations in which it is not desirable for the auto-pilotto control the aircraft, such as take-off or landing in which emergencymaneuvers are more likely to be required, the aircraft's flight controlsystem can be implemented to switch the operator 146 into the controlloop with units 144 and 148 as shown in FIG. 11. In this configuration,control and response characteristic(s) generated by the operator arehedged by the hedge unit 20. One barrier to implementation of adaptivecontrol systems in contexts such as aircraft is the stringent testingand certification required of adaptive control systems. Certification ismade difficult by the fact that it may be exceedingly difficult orimpossible to subject the adaptive control system to all plant states itis likely to encounter. The configuration of FIG. 11 provides theadvantage of permitting the use of an adaptive control system in whichthe pilot operator can control the aircraft without causing the controlsystem to adapt to the pilot's control and response. Accordingly, theconfiguration of FIG. 11 should facilitate testing and certification ofan adaptive control system incorporating the features of the unit 142 inFIG. 11.

The adaptive control system 10 can be used in numerous applications. Forexample, the plant 12 can be a manned or unmanned vehicle. Such vehiclecan be an aircraft, spacecraft, missile, or guided ordinance. Ingeneral, the adaptive control system 10 is assigned to control onedegree of freedom of the plant 12. The actuator 16, the sensor 18, theoperator interface unit 28, the operator 30, and the command unit 32depend upon the nature of the plant 12 and the degree of freedom thereofto be controlled by the adaptive control system 10. For example, if theplant 12 is a guided vehicle such as an aircraft, spacecraft, missile orother guided ordinance, the actuator 16 could be a motor, a motor-drivenscrew, a hydraulic cylinder or other device attached to a controlsurface such as an aileron, rudder, or stabilizer. Alternatively, theactuator 16 could be a pump or valve that generates air jet(s) to changethe flow of air over the guided vehicle's surface, or a frame actuatorthat changes the shape of the guided vehicle's surface. In addition, theactuator 16 could be thrust controllers to control the direction ofthrust generated by a power plant of the aircraft. Such actuators can beused to control the degree of freedom (e.g., pitch, roll, or yaw) thatis controlled by the adaptive control system 10. In the guided vehiclecontext, the sensor 18 can be a gyroscope or other device to measure thedegree of freedom controlled by the actuator 16. In the case of a mannedvehicle, the operator 30 can be a human, the operator interface unit 28a display, and the command unit 32 a control stick and/or flight controlsystem, for example. If the plant 12 is an automobile, the actuator 16can be a valve for a fuel injection port, a hydraulic cylinder to move abraking element into contact with a brake drum, a transmission or otherelement. In this case, the sensor 18 can be a speedometer, a pressuresensor in an engine cylinder, an inertial sensor, or other elements. Theplant 12 could also be a satellite, and the actuator 16 could be athruster to orient and position the satellite in orbit. The satellite'sactuator 16 could be a motor-driven electromechanical device to positiona solar panel or transceiver unit in a desired direction. In thesatellite context, the sensor 18 could be a gyroscope, for example. Asanother example, the operator 30 can be a combination of an auto-pilotand a human operator to take control of the plant in circumstances inwhich the auto-pilot is not to control the plant. Such implementationcan be used in aircraft, for example. The command unit 32 can beprogrammed to switch control between a machine and human operator tocontrol the aircraft plant 12. The hedge unit 20 can generate the hedgesignal to hedge characteristics of the human control of the command unit32 for stable control of the aircraft plant. It should be understoodthat the use of a vehicle context in the foregoing description isexemplary only, and is not intended to limit the scope or context inwhich the invented adaptive control system 10 can be used. Those ofordinary skill in the art should understand that the system 10 can beused in numerous other contexts and environments, such as manufacturingplants, power generation stations, and numerous other types of plants.

Any trademarks listed herein are the property of their respectiveowners, and reference herein to such trademarks is intended only toindicate the source of a particular product or service.

The many features and advantages of the present invention are apparentfrom the detailed specification and it is intended by the appendedclaims to cover all such features and advantages of the describedmethods and apparatus which follow in the true scope and spirit of theinvention. Further, since numerous modifications and changes willreadily occur to those of ordinary skill in the art, it is not desiredto limit the invention to the exact implementation and operationillustrated and described. Accordingly, all suitable modifications andequivalents may be resorted to as falling within the scope and spirit ofthe invention.

What is claimed is:
 1. A method executed by an adaptive control system,the method comprising the steps of: a) generating an input controlsignal based on at least one of a reference model state signal, acommanded state signal, a plant state signal, and an adaptive controlsignal; b) generating a command control signal based on at least one ofa commanded state signal, a plant state signal, an adaptive controlsignal, and further based on control allocation and a controlcharacteristic of a controller used to generate the command controlsignal; c) supplying the command control signal to an actuator; d)controlling a state of the plant based on the command control signal; e)sensing a state of the plant; f) generating a plant state signal basedon the sensing of the step (e); g) generating a first signal based onthe input control signal, the plant state signal, and a plant modelwithout a plant characteristic for which the adaptive control system isnot to adapt; h) generating a second signal based on the command controlsignal, the plant state signal, and a plant model with the plantcharacteristic for which the adaptive control system is to adapt; i)generating a hedge signal by differencing the first and second signals;j) generating a reference model state signal by modifying the commandedstate signal with the hedge signal to include the effect of the controlallocation and control characteristic on plant state from the referencemodel state signal; k) comparing the plant state signal and thereference model state signal; l) generating a tracking error signalbased on the comparing of the step (k); and m) generating the adaptivecontrol signal based on the tracking error signal.
 2. A method asclaimed in claim 1 further comprising the step of: n) generating thereference model signal based on the commanded state signal, the hedgesignal, and a reference model representing the target response of theplant, the reference model signal used in the step (a) to generate theinput control signal.
 3. A method as claimed in claim 1 furthercomprising the step of: n) generating the reference model signal basedon the commanded state signal, the hedge signal, and a reference modelrepresenting the target response of the plant, the reference modelsignal used in the step (b) to generate the command control signal.
 4. Amethod as claimed in claim 1 further comprising the step of: n)generating a linear control signal based on the tracking error signal;o) generating a reference model signal based on the commanded statesignal, the hedge signal, and a reference model; and p) generating apseudo-control signal based on the linear control signal, the referencemodel signal, and the adaptive control signal, the pseudo-control signalused in the generation of the adaptive control signal in the step (m).5. A method as claimed in claim 1 further comprising the step of: n)generating the commanded state signal based on a control action from anoperator.
 6. A method as claimed in claim 1 further comprising the stepof: n) generating the commanded state signal based on a signal generatedby an operator that is a computer.
 7. A method as claimed in claim 1further comprising the step of n) generating a display for an operatorbased on the input control signal, the operator generating the commandcontrol signal based on the display.
 8. A method as claimed in claim 1wherein the plant is an aircraft and/or spacecraft.
 9. A method asclaimed in claim 1 wherein the plant is an automobile.
 10. A method asclaimed in claim 1 wherein the plant is an unmanned vehicle.
 11. Amethod as claimed in claim 4 wherein the adaptive control signal isgenerated in the step (m) based on the plant state signal, the step (m)performed by a neural network having connection weights adjusted basedon the tracking error signal and the pseudo-control signal, the neuralnetwork mapping the plant state signal to the adaptive control signal inthe performance of the step (m).
 12. A method as claimed in claim 4wherein the plant state signal is used in the step (m) to generate theadaptive control signal.
 13. A method as claimed in claim 5 wherein theoperator is human, the method further comprising the step of: o)generating a display based on the plant state signal, the display usedby the operator to generate the commanded state signal in the step (n).14. An adaptive control system coupled to receive a command state signalindicative of a target state of a plant controlled by the adaptivecontrol system, the adaptive control system comprising: a controllercoupled to receive the commanded state signal, a plant state signal, andan adaptive control signal, the controller generating an input commandsignal based on the commanded state signal, the plant state signal, theadaptive control signal, and a control model, and the controllergenerating a command control signal based on the commanded state signal,the plant state signal, the adaptive control signal, the control model,control allocation of the controller, and at least one controlcharacteristic of the controller, the controller coupled to supply thecommand control signal to the plant to control the plant's state; anactuator coupled to receive the command control signal, and affectingphysical control of the plant's state based on the command controlsignal; a sensor coupled to sense the plant state, and generating aplant state signal based on the sensed plant state; a hedge unit coupledto receive the input control signal, the command control signal, and theplant state signal, and generating a hedge signal to modify the commandstate signal based on the input control signal, the command controlsignal, the plant state signal, and a hedge model indicative of acharacteristic of at least one of the plant and the adaptive controlsystem, to remove the effect of the characteristic on a tracking errorsignal; a reference model unit coupled to receive the command statesignal and the hedge signal, the reference model unit generating areference model state signal based on the commanded state signal and ahedge signal; a comparator unit coupled to receive the reference modelstate signal and the plant state signal, and generating a tracking errorsignal based on a difference between the plant state signal and thereference model state signal; and an adaptation law unit coupled toreceive the tracking error signal, and generating the adaptive controlsignal based on the tracking error signal, the adaptation law unitcoupled to supply the adaptive control signal to the controller.
 15. Anadaptive control system as claimed in claim 14 wherein the controllergenerates the input control signal and the command control signalfurther based on the reference model state signal.
 16. An adaptivecontrol system as claimed in claim 14 wherein the characteristic is atime delay between generation of the commanded state signal by thecontroller at a time; and receipt by the controller of the plant statesignal resulting from the commanded state signal generated at the time.17. An adaptive control system as claimed in claim 14 wherein thecharacteristic is a time delay between generation of a state by theplant in response to the command control signal, and sensing of thestate of the plant resulting from the command control signal.
 18. Anadaptive control system as claimed in claim 14 wherein thecharacteristic pertains to a control limit of the actuator used tocontrol the plant.
 19. An adaptive control system as claimed in claim 14wherein the commanded state signal is generated by an operator, theadaptive control system further comprising: an operator interface unitcoupled to receive the plant state signal, the operator interface unitrelaying the plant state to the operator; and a command unit operable bythe operator, and generating the command state signal based on theoperator's control action.
 20. An adaptive control system as claimed inclaim 14 wherein the operator interface is a display generated based onthe plant state signal, and the operator is a human being that generatesthe control action to the command unit to generate the commanded statesignal.
 21. An adaptive control system as claimed in claim 14 whereinthe commanded state signal is generated by a machine operator based onthe plant state signal.
 22. An adaptive control system as claimed inclaim 14 wherein the adaptation law unit comprises a neural networkhaving connection weights determined by the tracking error signal, theneural network mapping the plant state signal to the adaptive controlsignal based on the connection weights to generate the adaptive controlsignal.
 23. An adaptive control system as claimed in claim 14 whereinthe controller includes a dynamic inversion unit to generate the commandcontrol signal.
 24. An adaptive control system as claimed in claim 14wherein the input control signal is used to generate a display, and theoperator generates a command control signal based on the display.
 25. Anadaptive control system as claimed in claim 14 wherein the plant is anaircraft and/or spacecraft.
 26. An adaptive control system as claimed inclaim 14 wherein the plant is an automobile.
 27. An adaptive controlsystem as claimed in claim 14 wherein the plant is an unmanned vehiclepositioned remotely from the operator.
 28. An adaptive control system asclaimed in claim 18 wherein the control limit pertains to actuator endpoints.
 29. An adaptive control system as claimed in claim 18 whereinthe control limit pertains to actuator dynamics.
 30. An adaptive controlsystem as claimed in claim 18 wherein the control limit pertains to arate limit of the actuator.
 31. An adaptive control system as claimed inclaim 18 wherein the control limit pertains to quantization effects ofthe actuator.
 32. An adaptive control system as claimed in claim 22wherein the controller generates a pseudo-control signal based on thecommanded state signal and the plant state signal, the controllercoupled to supply the pseudo-control signal to the neural network toadjust the connection weights of the neural network.